Elasto-plastic stress distributions in adhesively bonded double lap joints

Elasto-plastic stress analysis is an important solution for a used ductile adhesive in single or double lap solutions. After loading, the joint strength can be increased by residual stresses. In this study, an elasto-plastic stress analyses of the shear and peel stresses are carried out in a double-lap joint. The adhesive material is chosen as a ductile material which is DP460. Elasto-plastic solution of the shear stress is obtained in a simple and accurate form in one dimensional case. Then, the solution of the peel stress is performed by considering the shear stress in the elasto-plastic form. In this solution, the boundary conditions are satisfied by the Newton–Raphson method. A good agreement is obtained between these analytical and numerical (ANSYS 10) solutions. The values are calculated highest at the ends of the adhesive.     

An analytical solution for the analysis of symmetric composite adhesively bonded joints

Analytical solutions for adhesively bonded balanced composite and metallic joints are presented in this paper. The classical laminate plate theory and adhesive interface constitutive model are employed for this deduction. Both theoretical and numerical (finite element analysis) studies of the balanced joints are conducted to reveal the adhesive peel and shear stresses. The methodology can be extended to the application of various joint configurations, such as single-lap and single-strap joints to name a few. The methodology was used to evaluate stresses in several balanced adhesively bonded metallic and composite joints subjected to the tensile, moment and transverse shear loadings. The results showed good agreements with those obtained through FEM.     

粘着应力拉伸过程数值模拟及粘着应力模型

为了精确计算粘性介质压力成形过程中粘性介质/板材界面粘性附着作用,分析了压力、剪切速率、温度等因素对粘着应力的影响,提出了粘着应力计算模型.将提出的粘着应力模型引入有限元分析软件中,对粘着应力拉伸过程进行了数值模拟,并将计算结果与试验结果进行对比,验证提出模型的可靠性.结果表明:采用建立的模型预测的试样伸长量及应变分布与实验测量结果具有较好的一致性.说明建立的粘着应力模型可以准确反映板材/粘性介质界面粘着应力大小,为精确模拟粘性介质压力成形过程提供了模型.     

The analysis of elastic-plastic adhesive stress in bonded lap joints in FRP structures

The majority of researchers who investigate the theoretical distribution of adhesive stresses in bonded lap joints assume that the adhesive behaves as a linear elastic material. While this assumption does provide useful information, for example, the intensities of stress concentrations and their locations, the results do not reflect the true stress distribution or behaviour at appreciable levels of loading. Practical joints using typical structural adhesives will incur considerable adhesive yielding as loading is increased to failure. The analysis must, therefore, include plastic yielding of the adhesive.This paper presents two analytical techniques, namely, the classical and finite element theories, which will be used to determine elastic-plastic adhesive stress distribution in bonded lap joints. The theoretical work will consider the single, double and tubular lap configurations having both similar and dissimilar adherends. Case studies will be presented to illustrate the development of adhesive yielding and to compare the different analytical techniques.The classical approach was found to be intractable to a closed form solution and consequently a numerical method was employed.     

Analytical modelling of the electromechanical behaviour of surface-bonded piezoelectric actuators including the adhesive layer

The behaviour of a piezoelectric actuator is strongly affected by the bonding condition along the interface between the actuator and the host structure. The current paper represents an analytical study of the static effect of the mechanical and geometrical properties of the adhesive layer on the coupled electromechanical behaviour of a thin piezoceramic actuator bonded to an elastic medium. An actuator model with an imperfect adhesive bonding layer, which undergoes a shear deformation, is proposed to simulate the two dimensional electromechanical behaviour of the integrated system. Analytical solution of the problem is provided by solving the resulting integral equations in terms of the interfacial stress. Numerical simulation is conducted to study the effect of the bonding layer upon the actuation process. The effect of interfacial debonding on the response of the layered structure and on the interlaminar strain and stress transfer mechanisms is discussed.     

Accurate evaluation of 3D stress fields in adhesive bonded joints via higher-order FE models

Abstract

The accurate representation of the 3D stress fields at the bonded areas of adhesive joints is essential for their design and strength evaluation. In the present study, higher-order beam models developed in the framework of the Carrera Unified Formulation are employed to reduce the complexity and computational cost of numerical simulations on adhesive joints. The different components of the adhesive joint, i.e. adherends and adhesive, are modeled as beams with independent kinematics based on the Hierarchical Legendre Expansion (HLE). HLE models make use of a hierarchical polynomial expansion over the cross-section of the beam, thus allowing for the control of the accuracy of the stress solutions via the polynomial expansion. Recalling the Finite Element method, the beam axis is discretized by means of 1D elements. In this manner, generic geometries of the adhesive bonded joints can be studied. The proposed model is assessed through comparison against numerical and analytical references from the literature for single lap and double lap joints. Finally, a detailed 3D analysis is performed on the single lap joint problem, showing that the stress gradients along the adhesive are correctly and efficiently described if the proposed methodology is employed.     

The effects of thermal cycle and nanostructure reinforcement on the shear load in adhesively bonded joints

Abstract

In this study, the shear strength of a nanocomposite adhesive was experimentally and numerically investigated under ambient temperature and thermal cycling conditions. This study used the Thick Adherend Shear Test method, which is commonly used to determine the shear stress–displacement of adhesives. Shear–displacement was determined by an extensometer to accurately compare results obtained from the Thick Adherend Shear Test results for joints with numerical analyses. As a result, when the shear failure load obtained from experiments was examined, the nanocomposite adhesives, obtained by adding a nanostructure into the adhesive, improved both the ambient temperature and thermal cycling performances of the joints.     

A Cell Method Stress Analysis in Thin Floor Tiles Subjected to Temperature Variation

The Cell Method is applied in order to model the debonding mechanism in ceramic floor tiles subjected to positive thermal variation. The causes of thermal debonding, very usual in radiant heat floors, have not been fully clarified at the moment. There exist only a few simplified analytical approaches that assimilate this problem to an eccentric tile compression, but these approaches introduce axial forces that, in reality, do not exist. In our work we have abandoned the simplified closed form solution in favor of a numerical solution, which models the interaction between tiles and sub-base more realistically, when the positive thermal variation increases the volume of the sub-base. The thermal problem has been approached as a contact problem in a composite structure. In particular, the kinematic and equilibrium conditions have been imposed at the interface between lower part, which is the sub-base, and the upper part, which is composed by the adhesive, the tiles, and the grouting between the tiles. The failure condition has been studied in the Mohr-Coulomb plane by using the Leon criterion, a unifying criterion that combines the shear stress with traction and compression. Therefore, we employed a unique failure criterion both for the nodes at the interface between sub-base and adhesive (which undergo a shear/tensile failure or a shear failure) and the nodes at the interface between tiles and grouting (which undergo a tensile failure). This allowed us to model the tile debonding both in the horizontal and in the vertical interfaces, while previous FEM codes treated the tile debonding only on the horizontal interfaces. The numerical analyses were performed in parametric modality, by varying the geometric and mechanical characteristics of the model. Particular attention was devoted to the modeling of thin tiles, a new type of ceramic tiles, for which there are no yet consensus standards.     

Through-thickness strain field measurement in a composite/aluminium adhesive joint

This paper presents an experimental procedure, which enables us to assess the shear strain field in an adhesive joint between composite and aluminium. In practice, this strain field is representative of the progressive stress transfer between a loaded structure and a composite patch used for reinforcement purposes. Digital image correlation (DIC) is used to measure the displacement field through the thickness of a patched specimen subjected to a tensile test. The shear strain field derives from the measured displacement field. The shear strain clearly decreases when the distance from the free edge of the adhesive increases, as predicted by numerical and analytical models of the joint. These measurements are used to estimate the in situ shear modulus of the adhesive. It is observed that the shear modulus decreases when the shear stress increases, thereby illustrating the non-linear response of the adhesive.     

Impact rupture of structural adhesive joints under different stress combinations

The paper reports the results of an experimental study on bonded joints, carried out by means of an instrumented impact pendulum, equipped to load overlap specimens in shear. Such testing configuration is the most adequate and natural to study the possible modifications of the behavior of the joint, changing from static to dynamic loading condition, keeping the same specimen type. The specimens were steel strips bonded by an epoxy adhesive (Hysol 3425). Several values of lap length, adhesive and adherends thickness were adopted, to achieve rupture under different peel and shear stress combinations. The stress state at rupture has been calculated by means of a structural solution. The results show that the failure points, in a chart having as axes the maximum values of peel and shear structural stress, lie outside the rectangular limit zone previously obtained under static conditions. Therefore, in spite of the concerns associated with the impact condition, the strength of the tested adhesive does not decrease with respect to the case of static loading. In alternative, also the evaluation of the stress intensity factor proves to be effective to predict failure in the considered cases.     

金属裂纹板复合材料单面胶接修补结构应力分析

考虑金属裂纹板复合材料单面胶接修补结构的几何非线性和边界条件,建立了考虑弯曲变形单面修补结构力学分析模型,计算出承受面内载荷时修补结构的弯矩和挠度,将补片自由端和金属板裂纹处的弯矩作为胶层应力控制微分方程的边界条件,推导出剪应力和剥离应力的解析解,及裂纹张开位移的表达式,并与有限元数值结果进行对比。分析结果表明,胶接修补结构应力分析理论模型和相关简化假设合理、正确。利用所建立的解析模型研究了金属裂纹复合材料单面胶接修补结构的应力分布特点及胶层主导破坏模式的失效机制,为胶接修补结构的承载能力分析以及结构改进设计提供了一定的理论依据。     

On the reduce of interfacial shear stresses in fiber reinforced polymer plate retrofitted concrete beams

One major problem when using bonded fiber reinforced polymer (FRP) plate is the presence of high interfacial shear stresses near the end of the composite (edge effect) which might govern the failure of the strengthening schedule. It is known that the decrease of plate thickness reduces the magnitude of stress concentration at plate ends. Another way is to use a plate end tapering. In this paper, the analytical solution of interfacial shear stresses obtained has been extended by a numerical procedure using the modal analysis of finite element method (FEM) in a retrofitted concrete (RC) beam with the FRP plate with tapered end, which can significantly reduce the stress concentration. This approach allows taking into consideration the variation of elastic properties of adhesive and plate as well as the complicated geometrical configurations and effects of thermal loads.     

Geometrical effects in adhesive joints

This paper is concerned with determining the effects of the geometry of the adherends, near the end of the bond line, upon the strength of a shear lap adhesive joint. The particular two dimensional elasto-static boundary value problem of a wedge bonded to a half plane along a finite length is considered in detail. The connection transmits a resultant normal and shear force as well as a moment. A dual integral equation formulation is used and the mathematical problem is reduced to the numerical solution of simultaneous Fredholm integral equations of the second kind. Numerical results are presented for all of the stress intensity factors and the character of the stress field is discussed in detail. It is shown that if the moment, shear and normal resultants transmitted across the bond line satisfy certain relations, then the singular stress field at the ends of the bond line can be eliminated.     

内嵌CFRP筋加固宽缺口混凝土梁内力解析与试验研究

针对内嵌碳纤维增强塑料筋加固宽缺口混凝土梁体系,对碳纤维增强塑料筋、胶粘剂及混凝土三种介质两个界面的内力进行了力学解析分析,分析研究表明:剪应力是碳纤维增强塑料筋-胶粘剂-混凝土界面的粘结应力的主体,由内嵌加固宽缺口梁破坏试验可直接获取界面的剥离承载力;碳纤维增强塑料筋的受力相当于外表受到剪应力和正应力的圆柱体,剪应力靠胶结力提供,筋表面的平均剪应力可以通过宽缺口处外露部分的应变片实测得到,且与试验结果吻合较好,筋表面正应力的作用可以忽略;碳纤维筋横截面上的正应力在筋的长度方向成幂指数分布,沿筋截面径向分布不均匀,这导致其横截面中心的变形滞后于筋边缘的变形;槽内胶凝固后的内聚体是一个断面内圆外方的柱体,可以假定为是近似的厚壁圆筒,胶内聚体内的切向和径向应力对胶内聚体的剪切变形几乎没有影响;界面剥离破坏在比邻界面的混凝土中发生,因此混凝土强度将显著影响界面粘结性能与剥离承载力。     

Glued-in-rod timber joints: analytical model and finite element simulation

In this paper, a closed form analytical solution for glued-in-rod (GiR) joints is derived by solving the governing differential equations and accurately applying the boundary conditions in a cylindrical coordinate system for a GiR joint comprising of a rod, adhesive (glue) and timber. The results of the analytical model are compared with 3D continuum finite element simulations and it is shown that the closed-form solution developed can estimate the stress distribution in the adhesive and adherents (rod and timber) with good accuracy. Furthermore, the stiffness of GiR timber joints can be obtained from this analytical model. Closed-form solutions for pull–pull and pull–push test setup configurations are compared and it is shown that the maximum shear stress in the adhesive-adherent interface in a pull–push configuration is around 20% higher than that of the pull–pull counterpart. The typically (around 20%) lower strength of GiR joints in pull–push experiments compared to that of pull–pull tests can be attributed to this higher maximum shear stress which is predicted by the analytical model. A parametric study is carried out using the FE and analytical models and the effects of different variables on the distribution of stresses in the adhesive and adherents are studied.     

Elastic problem of an adhesion crack in T-junction of two orthotropic thin plates

In this study, the general solution is derived for stresses in a T-junction of two thin plates with an adhesion crack. The plates are orthotropic, and shear force is applied to the crack surface. The analysis is based on the supposition that the stresses in each plate can be approximated by the condition of plane stress. The results obtained are verified through numerical calculation using the finite element method. A singular stress field is obtained from the solution in the vicinity of a crack tip.     

General solution of stresses due to an adhesion crack for T-shaped junction of two plates

In this study, the general solution of stresses is derived for a T-shaped junction consisting of two thin plates with an adhesion crack. A shear force is applied to the crack surface. The analysis is based on the supposition that the stresses in each plate can be approximated by the plane stress condition. The results obtained are verified by a numerical calculation based on the finite element method. Moreover, a singular stress field is obtained from the solution for the vicinity of the crack.     

Stress analysis of adhesively-bonded lap joints

The adhesively-bonded joints considered in this investigation include single-lap joint and double-lap joint. A simplified one-dimensional model based on the classical elasticity theory is presented. The shear deformation in the adhesive is assumed constant across the adhesive thickness. The analytical solutions of shear stress in the adhesive and longitudinal stress in the adherend are obtained and compared with the numerical solutions determined by the two-dimensional finite element method.     

Analytical investigation and numerical simulation of the stress–strain state in mechanically heterogeneous welded joints with a single-V butt weld

This paper aims to investigate the stress–strain state in mechanically heterogeneous welded joints with a single-V butt weld by an analytical model along with a numerical simulation. Analytical expressions for the stress–strain state in both the weld and the main material are proposed. In order to verify the proposed expressions, a numerical simulation of the stress–strain state in a mild welded joint with a single-V butt weld was carried out on the basis of the finite element method and the results were compared with the analytical solution obtained applying the proposed analytical model. EP-787 and JONI 13/45А steels were used for the weld while 15X2MFА steel was used for the main material in the analysed welded joints. A comparison of the analytical solution with the finite element analysis results showed a good agreement. The proposed equations could be used in design practice for calculations of the stress–strain state in welded joints.     

Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp

This study investigates the problem of sliding frictional contact between a laterally graded elastic medium and a rigid circular stamp. Analytical and computational methods are developed to evaluate the contact stresses. In the analytical formulation, spatial variation in the shear modulus of the graded medium is represented by an exponential function, and Poisson’s ratio is taken as a constant. Coulomb’s dry friction law is assumed to hold within the contact area. The two-dimensional plane elasticity problem is formulated utilizing Fourier transforms, and the resulting Cauchy-type singular integral equation of the second type is solved by applying an expansion–collocation technique. The finite element method is used in the computational analysis of the contact problem. In the finite element model, continuous variation of the shear modulus is taken into account by specifying this property at the centroid of each finite element. The finite element-based solution procedure is verified by making comparisons to the results obtained through the analytical method. Numerical results generated for the laterally graded medium with an exponential variation in the shear modulus illustrate the influences of lateral gradation and coefficient of friction upon the contact stress distributions. The capability of the proposed finite element method is further demonstrated by providing numerical results for a laterally graded medium whose shear modulus is represented by a power function.